1. Field of the Invention
The invention pertains generally to moire interferometry, and more particularly to a portable moire interferometer and to a corresponding moire interferometric method.
2. Description of the Related Art
Moire interferometry is an optical technique for measuring the in-plane displacements of a specimen under load. As described, for example, in Chapter 4 of the book by Daniel Post, Bongtae Han and Peter Ifju entitled High Sensitivity Moire (Springer-Verlag, New York, 1994), and as depicted in FIG. 1, in moire interferometry the specimen surface of interest is provided with a crossed-line diffraction grating, i.e., a diffraction grating having grating lines in two orthogonal directions. This specimen grating deforms together with the specimen when the specimen is subjected to a mechanical or thermal load. Therefore, the in-plane deformations suffered by the specimen grating represent the in-plane deformations suffered by the specimen.
As depicted in FIG. 1, when measuring displacements in, for example, the X-direction via moire interferometry, two mutually coherent beams of light, B.sub.1 and B.sub.2, of identical wavelength, lambda.sub.x, which lie in the X-Z plane, are impinged upon the specimen grating. These beams are impinged at angles of, respectively, +alpha.sub.x and -alpha.sub.x, relative to the normal to the specimen surface, and each beam is reflectively diffracted by the specimen grating. Significantly, the angles +alpha.sub.x and -alpha.sub.x (which are of equal magnitudes) are chosen so that each incident beam results in a diffraction order, i.e., the +1 diffraction order or the -1 diffraction order, which emerges from the specimen grating perpendicularly to the specimen surface. Such a choice implies that alpha.sub.x, lambda.sub.x and the specimen grating frequency in the X-direction, f.sub.sx, satisfy the relationship EQU sin alpha.sub.x =lambda.sub.x *f.sub.sx ( 1)
The resulting two diffraction orders then interfere with one another to produce a moire fringe pattern, which is readily imaged with a camera, as depicted in FIG. 1. It should be noted that such a fringe pattern constitutes a contour map where displacements in the X-direction, U, are related to fringe order, N.sub.x, by EQU U=N.sub.x /2f.sub.sx. ( 2)
If displacements in the Y-direction are to be measured, then two mutually coherent beams of light, B.sub.3 and B.sub.4, of identical wavelength, lambda.sub.y, which lie in the Y-Z plane, are impinged upon the specimen grating. Again, the beams B.sub.3 and B.sub.4 are impinged at angles of, respectively, +alpha.sub.y and -alpha.sub.y, relative to the normal to the specimen surface. As before, the angles +alpha.sub.y and -alpha.sub.y are chosen so that each incident beam results in a diffraction order which emerges from the specimen grating, perpendicularly to the specimen surface. This implies that alpha.sub.y, lambda.sub.y and the specimen grating frequency in the Y-direction, f.sub.sy satisfy the relationship EQU sin alpha.sub.y =lambda.sub.y *f.sub.sy ( 3)
The interference between the resulting two diffraction orders then produces a moire fringe pattern which is also readily imaged with a camera. As before, such a fringe pattern constitutes a contour map where displacements in the Y-direction, V, are related to fringe order, N.sub.y, by EQU V=N.sub.y /2f.sub.sy ( 4)
Obviously, if the wavelengths lambda.sub.x and lambda.sub.y are equal to one another, and these identical wavelengths are denoted by lambda, and if the specimen grating frequencies f.sub.sx and f.sub.sy are equal to one another, and these identical frequencies are denoted by f.sub.s, then it follows from Eqs. (1) and (3) that EQU sin alpha.sub.x =sin alpha.sub.y =lambda*f.sub.s, (5)
and therefore EQU alpha.sub.x =alpha.sub.y =alpha. (6)
In addition, from Eqs (2) and (4), it follows that EQU U=N.sub.x /2f.sub.s ( 7)
and EQU V=N.sub.y /2f.sub.s. (8)
Interestingly, the concept of a virtual diffraction grating is sometimes used to explain the above-described diffraction and interference phenomena. That is, it is sometimes imagined that each pair of incident, coherent beams of light, e.g., the pair B.sub.1 and B.sub.2, initially interfere with one another in front of the specimen grating to form a virtual diffraction grating having a grating frequency, f, where EQU f=2*sin alpha/lambda=2*f.sub.s. (9)
It is then imagined that the virtual grating is superimposed upon the specimen grating, and the interaction between the two gratings forms a fringe pattern.
With reference now to FIG. 2, a conventional moire interferometer 10 typically includes a source of coherent light, such as a laser 20. This source serves to produce a collimated beam of coherent light which is impinged upon a beam splitter 30. The latter serves to creates two mutually coherent beams of light, which are directed to mirrors 40 and 50. These mirrors then serve to direct the two coherent beams of light to a specimen diffraction grating 70 mounted on a specimen 60. The two resulting diffraction orders which emerge from the specimen diffraction grating 70 interfere with each other to produce a moire fringe pattern, which is imaged with a camera.
It should be noted that prior to subjecting the specimen 60 to a mechanical or thermal load and imaging the corresponding moire fringe pattern, it is essential that the positions of the mirrors 40 and 50 be initially adjusted to achieve a null field. That is, in the absence of a load on the specimen 60, the positions of the mirrors 40 and 50 must be adjusted so as to achieve a moire fringe pattern which has no fringes, or no more than a minimum number of fringes. Otherwise, the moire fringe pattern produced when the specimen is subjected to a load will contain fringes which are unrelated to the load and are therefore misleading.
Although not shown in FIG. 2, a conventional moire interferometer includes the optical elements, described above, mounted on a relatively large optical table. Consequently, such a conventional moire interferometer is not at all portable, which limits its utility. Moreover, the optical elements of a conventional moire interferometer are necessarily exposed to the surrounding air, and therefore to air currents. But, such air currents can induce changes in refractive index which, in turn, can, for example, alter the optical path length of one of the beams incident on the specimen diffraction grating. Such a change in optical path length can introduce significant errors into the corresponding moire fringe pattern.
One attempt to overcome the lack of portability of conventional moire interferometer is described by D. Mollenhauer, P. G. Ifju and B. Han in "A Compact, Economical and Versatile Moire Interferometer", Proc. 1993 SEM Spring Conference on Experimental Mechanics, Society for Experimental Mechanics, Bethel, Conn., pp. 954-963 (1993). Here, the authors describe a new design for what is, in effect, a portable moire interferometer. In this design, the main structural feature is an aluminum ring, on which all of the optical elements are mounted. One of these optical elements is a crossed-line reference diffraction grating having a grating frequency of 1200 lines per millimeter (lines/mm).
In the operation of the above-described portable moire interferometer, a coherent light beam from a He-Ne laser is communicated by a single-mode optical fiber to optical elements mounted on the aluminum ring, which serve to direct this light beam at normal incidence onto the reference diffraction grating. This beam is then diffracted by both sets of grating lines to produce +1 and -1 diffraction orders in two orthogonal planes. These two pairs of mutually coherent beams of light are then directed by four mirrors mounted on the aluminum ring, two of which are manually adjustable, toward a crossed-line specimen diffraction grating. As a result, moire fringe patterns corresponding to in-plane displacements in both the X- and Y-directions are achieved.
While the above-described moire interferometer is portable and therefore overcomes one of the disadvantages associated with conventional moire interferometers, all of the optical elements of this moire interferometer are still exposed to the surrounding air. Therefore, this moire interferometer is still subject to undesirable changes in refractive index associated with air currents.
Thus, those engaged in the development of moire interferometry have sought, thus far without success, moire interferometers which are both portable and shielded from the surrounding Environment.